I agree with dirktheman here if we're talking about hosting a non-static website. Getting setup with EC2 is a huge pain if you don't know what you are doing. I really like Heroku for simple apps, but something like Linode makes a lot of sense if you wanna have more control over the server.

But I also agree with the parent comment about AWS S3 for static website. If you are setting up a static website with just HTML and CSS, S3 is the way to go. I do this for my homepage and it was very easy to setup and costs me about $0.52/month.

Added benefits are that you can use Cloudfront for CDN which also offers HTTPS. Some guides:

Example: Setting Up a Static Website Using a Custom Domain http://docs.aws.amazon.com/AmazonS3/latest/dev/website-hosti...

Using CloudFront with Amazon S3 http://docs.aws.amazon.com/AmazonCloudFront/latest/Developer...

Using HTTPS with CloudFront http://docs.aws.amazon.com/AmazonCloudFront/latest/Developer...

To the OP, I'm not sure what your experience level is, but if you consider yourself a beginner and you don't know what any of these terms mean, feel free to ping me if you have any questions!